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Dynamic programming (DP) is a fundamental tool used across many engineering fields. The main goal of DP is to solve Bellman's optimality equations for a given Markov decision process (MDP). Standard methods like policy iteration exploit the…
We introduce a learning-based framework to optimize tensor programs for deep learning workloads. Efficient implementations of tensor operators, such as matrix multiplication and high dimensional convolution, are key enablers of effective…
Domain decomposition methods (DDMs) are popular solvers for discretized systems of partial differential equations (PDEs), with one-level and multilevel variants. These solvers rely on several algorithmic and mathematical parameters,…
Online linear programming (OLP) has found broad applications in revenue management and resource allocation. State-of-the-art OLP algorithms achieve low regret by repeatedly solving linear programming (LP) subproblems that incorporate…
In the area of parameterized complexity, to cope with NP-Hard problems, we introduce a parameter k besides the input size n, and we aim to design algorithms (called FPT algorithms) that run in O(f(k)n^d) time for some function f(k) and…
Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks,…
We propose a novel paradigm for solving Inductive Logic Programming (ILP) problems via deep recurrent neural networks. This proposed ILP solver is designed based on differentiable implementation of the deduction via forward chaining. In…
This letter investigates a sum rate maximizationproblem in an intelligent reflective surface (IRS) assisted non-orthogonal multiple access (NOMA) downlink network. Specif-ically, the sum rate of all the users is maximized by…
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…
This paper investigates the general problem of resource allocation for mitigating channel fading effects in Free Space Optical (FSO) communications. The resource allocation problem is modeled as the constrained stochastic optimization…
Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but…
The exponential growth in the size and complexity of Large Language Models (LLMs) has introduced unprecedented challenges in their deployment and operational management. Traditional MLOps approaches often fail to efficiently handle the…
Offline reinforcement learning (RL) aims to find an optimal policy for Markov decision processes (MDPs) using a pre-collected dataset. In this work, we revisit the linear programming (LP) reformulation of Markov decision processes for…
In recent years, deep convolutional neural network-based segmentation methods have achieved state-of-the-art performance for many medical analysis tasks. However, most of these approaches rely on optimizing the U-Net structure or adding new…
The generalized Lasso is a remarkably versatile and extensively utilized model across a broad spectrum of domains, including statistics, machine learning, and image science. Among the optimization techniques employed to address the…
This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…
This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural…
Fractional Gradient Descent (FGD) offers a novel and promising way to accelerate optimization by incorporating fractional calculus into machine learning. Although FGD has shown encouraging initial results across various optimization tasks,…
We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient…
Large language models (LLMs) are still struggling in aligning with human preference in complex tasks and scenarios. They are prone to overfit into the unexpected patterns or superficial styles in the training data. We conduct an empirical…